Mathematics Syllabus – S4-S5 6 Periods (6P)

Schola Europaea / Office of the Secretary-GeneralPedagogical Development UnitRef.: 2019-01-D-49-en-4Orig.: ENMathematics Syllabus – S4-S516 Periods (6P)Approved by the Joint Teaching Committee at its meeting of 7 and 8February 2019 in BrusselsEntry into force on 1 September 2019 for S4on 1 September 2020 for S5The document “Mathematics Syllabus – S5 - 6 Periods” (ref. 2019-01-D-49-en-3) was approved by the JointTeaching Committee at its meeting of 13 and 14 February 2020 in Brussels12019-01-D-49-en-4

Europeans Schools - Mathematics SyllabusYear S4-S5 – 6 PTable of contents1.General Objectives . 32.Didactical Principles . 43.Learning Objectives . 64.5.3.1.Competences . 63.2.Cross-cutting concepts . 7Content . 84.1.Topics . 84.2.Tables. 8Assessment . 355.1.Attainment Descriptors . 36Annex 1: Suggested time frame . 38Annex 2: Modelling . 392019-01-D-49-en-42/40

1. General ObjectivesThe European Schools have the two objectives of providing formal education and ofencouraging pupils’ personal development in a wider social and cultural context. Formaleducation involves the acquisition of competences (knowledge, skills and attitudes) across arange of domains. Personal development takes place in a variety of spiritual, moral, social andcultural contexts. It involves an awareness of appropriate behaviour, an understanding of theenvironment in which pupils live, and a development of their individual identity.These two objectives are nurtured in the context of an enhanced awareness of the richness ofEuropean culture. Awareness and experience of a shared European life should lead pupilstowards a greater respect for the traditions of each individual country and region in Europe, whiledeveloping and preserving their own national identities.The pupils of the European Schools are future citizens of Europe and the world. As such, theyneed a range of competences if they are to meet the challenges of a rapidly-changing world. In2006 the European Council and European Parliament adopted a European Framework for KeyCompetences for Lifelong Learning. It identifies eight key competences which all individualsneed for personal fulfilment and development, for active citizenship, for social inclusion and foremployment:1.2.3.4.5.6.7.8.Literacy competenceMultilingual competenceMathematical competence and competence in science, technology and engineeringDigital competencePersonal, social and learning to learn competenceCivic competenceEntrepreneurship competenceCultural awareness and expression competenceThe European Schools’ syllabuses seek to develop all of these key competences in the pupils.Key competences are that general, that we do not mention them all the time in the Science andMathematics syllabuses.2019-01-D-49-en-43/40

2. Didactical PrinciplesGeneralIn the description of the learning objectives, competences, connected to content, play an importantrole. This position in the learning objectives reflects the importance of competences acquisition inactual education. Exploratory activities by pupils support this acquisition of competences, such asin experimenting, designing, searching for explanations and discussing with peers and teachers.In science education, a teaching approach is recommended that helps pupils to get acquaintedwith concepts by having them observe, investigate and explain phenomena, followed by the stepto have them make abstractions and models. In mathematics education, investigations, makingabstractions and modelling are equally important. In these approaches, it is essential that amaximum of activity by pupils themselves is stimulated – not to be confused with an absentteacher: teacher guidance is an essential contribution to targeted stimulation of pupils' activities.The concept of inquiry-based learning (IBL) refers to these approaches. An overview of usefulliterature on this can be found in the PRIMAS guide for professional development ads/sites/323/2017/10/PRIMAS Guide-for-ProfessionalDevelopment-Providers-IBL 110510.pdfMathematicsCareful thought has been given to the content and the structure to where topics are first met in apupil’s time learning mathematics in secondary education. It is believed that this is a journey andif too much content is met at one point, there is a risk that it will not be adequately understood andthus a general mathematical concept will not be fully appreciated. By limiting the content of thissyllabus (found in section 4.2.) each year more time can be used to develop core mathematicalconcepts that may have been met before or new mathematical concepts introduced are givenample time for extension. It must be noted that extension activities are conducted at the discretionof the teacher, however, it is suggested that rather than look at a vertical approach to extension ahorizontal approach is used, thus giving the pupil a deeper understanding of the mathematicalconcept (in section 4 the word ‘limitation’ is used to ensure the extension does not go too far).Furthermore, to this point it is believed that with a focus on competences this syllabus canencourage pupils to have a greater enjoyment of mathematics, as they not only understand thecontent better but understand the historical context (where it is expected a history of mathematicscan be told over the cycles) and how the mathematics can be applied in other subjects, crosscutting (these can be seen in the fourth column in section 4.2.). As such the syllabuses havespecifically been designed with reflection to the key competences (section 1.) and the subjectspecific competences (section 3.1.). In some cases, the key competences are clear for examplethe numerous history suggested activities (shown by the icon) that maps to key competency8 (Cultural awareness and expression). In other areas the link may not be so apparent.One of the tasks in the pupil’s learning process is developing inference skills, analytical skills andstrategic thinking, which are linked to both the key and subject specific competences. This is theability to plan further steps in order to succeed solving a problem as well as dividing the processof solving more complex problems into smaller steps. A goal of teaching mathematics is to developpupil’s intuitions in mathematics appropriate for their age. The ability to understand and usemathematical concepts (e.g. angle, length, area, formulae and equations) is much more importantthan memorising formal definitions.This syllabus has also been written so that it can be accessible by teachers, parents and pupils.This is one reason why icons have been used (listed in section 4.2.). These icons represent2019-01-D-49-en-44/40

different areas of mathematics and are not necessarily connected to just one competency but cancover a number of competences.To ensure pupils have a good understanding of the mathematics the courses from S1 to S7 havebeen developed linearly with each year the work from the previous year is used as a foundationto build onto. Thus, it is essential before commencing a year the preceding course must havebeen covered or a course that is similar. The teacher is in the best position to understand thespecific needs of the class and before beginning a particular topic it is expected that pupils havethe pre-required knowledge. A refresh is always a good idea when meeting a concept for the firsttime in a while. It should be noted that revision is not included in the syllabus, however, asmentioned earlier about limiting new content, there is time to do this when needed.The use of technology and digital tools plays an important role in both theoretical and appliedmathematics, which is reflected in this syllabus. The pupils should get the opportunity to work andsolve problems with different tools such as spreadsheets, computer algebra system (CAS)software, dynamic geometric software (DGS), programming software or other software that areavailable in the respective schools. Technology and digital tools should be used to support andpromote pupils’ understanding, for example by visualising difficult concepts and providinginteractive and personalised learning opportunities, rather than as a substitute for understanding.Their use will also lead to improved digital competence.Teachers have full discretion with how to teach this course, materials to use and even thesequence the content is taught in. The content and the competencies (indicated in the tables insection 4.2., columns 2 and 3) to be covered is, however, mandatory.The S4 6 Period CourseThe S4 4 Period course has been developed alongside the 6 Period course where the core workis done in the 4 Period course, and the 6 Period course will explore the content in more depth.With this approach, changing between the courses is possible, with the understanding that pupilshaving studied the 6 Period course will often have a greater depth of understanding.Students opting for the 6 Period course should have already gained confidence in handling thebasic requirements in algebra, arithmetic and plane geometry from past years. Though a fewteaching periods are allocated to building upon the ground work of the previous years, the majorpart of the teaching time addresses new concepts such as functions and vectors or deepensunderstanding of statistics and probability. The students embarking on the 6 Period course shouldbe aware that this course is demanding and that they will have to dedicate a considerable part oftheir working time to it, especially because no other course has so many teaching periods in total.The S5 6 Period CourseThis course has been specifically written for those who will be studying fields where mathematicsplays a significant role. This includes all scientific studies, but also some fields of economics,finance and social studies, keeping in mind that the list is not exhaustive. In this course, togetherwith acquiring skills that are essential for their broader studies, students will also develop anunderstanding of the culture and value of mathematics for its own enjoyment. Though there is nonoticeable gap in difficulty between the 6 Period course in S4 and the 6 Period course in S5, thestudents should be aware that without a strong foundation from S4, they will struggle in S5.Pupils must note that the 4 Period and 6 Period courses in S5 are different. Thus, pupils wishingto study the 5 Period course in S6 will need to be aware of this before embarking on the 4 Periodcourse in not just S5 but S4 too.2019-01-D-49-en-45/40